A Lyapunov-type function for generalized dynamical systems without uniqueness
type: Item
instance of: scholarly article
title: A Lyapunov-type function for generalized dynamical systems without uniqueness
zbMATH Open document ID: 1089.34529
author: A. F. Filippov
published in: Differential Equations
publication date: 2005-06-17T00:00:00Z
review text: Generalized dynamic systems without uniqueness are considered. A function \(v(x)\) is constructed in the neighborhood of an asymptotically stable equilibrium. This function satisfies more weak conditions than Lyapunov's function (in general, \(v(x)\) can be discontinuous). The existence of such a function is a necessary and sufficient condition for asymptotic stability of the equilibrium. The results obtained are applicable to autonomous differential equations \[ \frac{dx}{dt}=f(x) \] with continuous \(f(x)\).
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 34A36
zbMATH DE Number: 2176579
zbMATH Keywords: generalized dynamical systems without uniqueness
reviewed by: Alexander O. Ignatyev
MaRDI profile type: Publication
DOI: 10.1023/B:DIEQ.0000008419.31585.2D
description: scientific article; zbMATH DE number 2176579